\begin{tikzpicture}
    \tkzDefPoints{0/0/B, 3/0/C}
    \tkzDefTriangle[two angles=60 and 75](B,C)  \tkzGetPoint{A}
    \tkzDefLine[altitude](B,A,C)  \tkzGetPoint{D}
    \tkzDefLine[altitude](A,B,C)  \tkzGetPoint{E}
    \tkzInterLL(A,D)(B,E)  \tkzGetPoint{H}

    \tkzDrawPolygon(A,B,C)
    \tkzDrawSegments(A,D  B,E)
    \tkzMarkRightAngle(A,D,B)
    \tkzMarkRightAngle(B,E,C)
    \tkzLabelPoints[above](A)
    \tkzLabelPoints[below](B,C,D)
    \tkzLabelPoints[right](E)
    \tkzLabelPoints[above left](H)
\end{tikzpicture}

